# Average Speed Of a and b where d and t is not given

1. Apr 17, 2012

### rajatbbsr

A body covers half its journey with a speed of a m/s and the other half with a speed of b m/s Calculate the average speed of the body during the whole journey

2. Apr 17, 2012

### Curious3141

What have you tried so far?

3. Apr 17, 2012

### rajatbbsr

(d1/t1+d2/t2)/2

4. Apr 17, 2012

### Steely Dan

The definition of average speed is

$$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{\Delta x}{t_1+t_2},$$

if we let $t_1$ and $t_2$ denote the times for the two parts of the trip. You'll lead yourself astray if you try to use shortcuts on calculating average speed.

5. Apr 17, 2012

### rajatbbsr

Can you please explain it to me couldn't get you

6. Apr 17, 2012

### Steely Dan

All I'm saying is that the formula I posted is the definition of average speed, the way it's commonly understood. Sometimes you can also calculate average speeds in physics I by appealing to the notion of "average" that you might already have in your head, like calculating the mean of a set of numbers. But you might get the wrong answer if you do it that way unless you're very careful. So use the physics definition that I posted instead of the algebraic mean definition. And that definition is just the total distance divided by the total amount of time.

7. Apr 17, 2012

### rajatbbsr

hmmm got you isn't the answer is d/(t1+t2) can it be more simplified

8. Apr 17, 2012

### Steely Dan

Yes, it has to be simplified. The goal here is to write the answer only in terms of a and b, since that's the only information you have, in the sense of actual numbers.

9. Apr 17, 2012

### rajatbbsr

10. Apr 17, 2012

### Steely Dan

That part is up to you :-)

But as a hint, start by assigning $d_1,t_1$ to the first part of the journey and $d_2,t_2$ to the second part of the journey, and $d,t$ to the full journey. And use the one piece of information you have regarding the connection between the two parts of the trip.

11. Apr 17, 2012

### Curious3141

The definition of average speed = total distance travelled/total time taken.

It's NOT simply the average of the speeds in different legs of the journey.

You've denoted the distance travelled in each leg by d1 and d2. Since you're given that the body covers half its journey in each leg, why not just denote the distance of a single leg by d?

OK, so the total distance is 2d.

Can you now find an expression for the time taken in each half of the journey in terms of its speed and the distance travelled?